Analog vs Digital Confusion

Thinking about adding Analog to my system, specifically a Turntable, budget is about 5K but I'm having some second thoughts and I'm hoping someone can help, specifically, how can the record sound better? Scenario; an album is released in both CD and Record, the recording is DDD mixed, mastered, etc in the digital domain. It seems to me that to make the master record the process would involve taking the digital recoding and adding an additional D/A process to cut the record? So, bottom line, how can the record sound better than the CD played on compitent CDP?
"Personally, I enjoy both formats, to a greater or lesser degree depending on the quality of the particular recording."

Al, that is very well said and I have recently adopted that philosophy.
Rpg, I have recently added vinyl, and can recommend it. It's heaps of fun, and I never cease being amazed that a squiggle in a piece of plastic can deliver so much information. In order to get great gear at a reasonable price get second hand. The only thing I would buy new is the cartridge, unless you know the person selling to you. For example-at present there is a Clearaudio Champion level II with Unify arm on this site for 2850, add a delos 1650, and that leaves you 2000 odd for a phono stage. May I recommend a SimAudio 5.3rs second hand should be just over 1000. The new 310 is just a cosmetic upgrade (new face plate) IMHO. I believe it is possible to get good and enjoyable, if not the "best", on your budget. I'm sure there are other great deals if you follow the smalls pages. It won't do away with your digital, but will almost certainly enhance your enjoyment of the hobby, and music. good luck.
Back to the original question-

If your total buget for an analog rig is $5k, meaning- turntable, tone arm, cartridge, phono stage and possibly a tone arm cable you may want to stick with a CDP if ultimate sound reproductive quality is your main objective.This is assuming your CDP is of reasonably high quality.

I listen almost exclusively to records, have a very well regarded and expensive CDP, and feel that you typically need to spend at LEAST three times the cost of your CDP for an analog rig that would best it. So, if you have a $5K CDP then you would need to invest $15K on all the above items to create an analog system which MAY better your digital. No guarantees it will, analog is a great deal more complicated than popping in a CD. It is, however, extremely rewarding when and if you get that turntable really singing.

Not trying to discourage a turntable purchase, just trying to address what you were asking for in your initial post.
I have never had an issue with pitch stability when using a TT.

As for vinyl v CD then as has been mentioned previously I think it is a preference thing.

I came to CD quite late and still have a largish vinyl collection so it made sense to invest in my analogue set up. My original experience with CD had always found me migrating back to vinyl.

More recently I have been able to improve on CD replay and this sounds very good now. If I had been able to achieve this level of reproduction before then I might not have pursued the analogue path quite so commitedly.

Starting from scratch with vinyl is quite daunting these days, there seems to be quite a premium attached to both 2nd hand and new vinyl LPs. I do buy some new vinyl but the majority of modern releases that interest me are only on CD.

On the equipment side, besides the TT and arm, one also needs to buy a phono stage and cartridge. Although there is a much wider choice of analogue gear now, to achieve
the best sound still requires quite an outlay.

Having a good CD set up means I am not solely reliant on the AP golden oldie re-releases etc, I have a lot of the originals anyway. I can buy newly recorded classical, jazz and world music on CD at a reasonable cost and enjoy listening to it all

So although I would not be without my TT to play my existing collection of rock, be bop, classical etc, it is nice to have the CD for newly purchased music.

The best sounding vinyl still outshine CD IMO but often CD runs the analogue very close. Everything is depended on the quality of the recording at the end of the day